What the wrapper does is “removing” Woo wrapper and adds in Theme specific ones, but only where it needs types of thing. The entire point behind is to have a layout that doesn’t break, at least that was what I’ve experienced with some Themes 🙂

Ulrich,
if all you want to do is make the checkout page full width, do it via css and the body class.

body.woocommerce-cart #content {width:100%;}

We’ve had no problems using CSS to fix many quirks of the WooCommerce layouts when we integrated it fully into Responsive LabZip.

If you use a child theme, remember that (to override default WooCommerce templates) you don’t need to use the folder name of “templates” when putting the replacement templates into a “woocommerce” folder in your child theme.

Just to clear this up, the checkout page is not a WooCommerce page per say. It’s a standard WordPress page containing a WooCommerce shortcode.

So if you want to manipulate the the layout for that page you should edit page.php using is_checkout() for the checkout specific bits. Or better yet you could create a custom template for the checkout and select that from the edit page screen.